Generalized Hasimoto transform of one-dimensional dispersive flows into compact Riemann surfaces

DOI10.3842/SIGMA.2008.044zbMath1147.35075arXiv0712.3105MaRDI QIDQ935729

Eiji Onodera

Publication date: 8 August 2008

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.3105

zbMATH Keywords

geometric analysismoving framevortex filamentSchrödinger mapHasimoto transformdispersive flow

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) NLS equations (nonlinear Schrödinger equations) (35Q55) Applications of differential geometry to physics (53Z05) Geometric theory, characteristics, transformations in context of PDEs (35A30)

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A fourth-order dispersive flow equation for closed curves on compact Riemann surfaces ⋮ Quasi‐Classical Approximation in Vortex Filament Dynamics. Integrable Systems, Gradient Catastrophe, and Flutter ⋮ A third order dispersive flow for closed curves into almost Hermitian manifolds ⋮ Uniqueness Of 1D generalized bi-Schrödinger flow ⋮ Local existence of a fourth-order dispersive curve flow on locally Hermitian symmetric spaces and its application ⋮ Fourth-order dispersive systems on the one-dimensional torus

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